LMFDB - Embedded newform 864.2.y.a.97.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(97,864)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("864.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.y (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			97.5
Character	$\chi$	$=$	864.97
Dual form			864.2.y.a.481.5

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.418682 - 1.68069i) q^{3} +(3.54422 + 1.28999i) q^{5} +(-0.131496 + 0.745751i) q^{7} +(-2.64941 - 1.40735i) q^{9} +O(q^{10})$	\(q+(0.418682 - 1.68069i) q^{3} +(3.54422 + 1.28999i) q^{5} +(-0.131496 + 0.745751i) q^{7} +(-2.64941 - 1.40735i) q^{9} +(5.73551 - 2.08756i) q^{11} +(-3.77411 + 3.16685i) q^{13} +(3.65197 - 5.41662i) q^{15} +(-0.681013 - 1.17955i) q^{17} +(2.71190 - 4.69715i) q^{19} +(1.19832 + 0.533236i) q^{21} +(0.406649 + 2.30622i) q^{23} +(7.06720 + 5.93008i) q^{25} +(-3.47457 + 3.86360i) q^{27} +(4.13561 + 3.47019i) q^{29} +(-0.295571 - 1.67627i) q^{31} +(-1.10717 - 10.5136i) q^{33} +(-1.42806 + 2.47348i) q^{35} +(1.11813 + 1.93666i) q^{37} +(3.74233 + 7.66899i) q^{39} +(-1.22528 + 1.02813i) q^{41} +(-5.88030 + 2.14026i) q^{43} +(-7.57463 - 8.40566i) q^{45} +(1.93713 - 10.9860i) q^{47} +(6.03899 + 2.19801i) q^{49} +(-2.26758 + 0.650713i) q^{51} -7.06071 q^{53} +23.0208 q^{55} +(-6.75901 - 6.52447i) q^{57} +(-11.6613 - 4.24435i) q^{59} +(0.963730 - 5.46558i) q^{61} +(1.39792 - 1.79074i) q^{63} +(-17.4615 + 6.35546i) q^{65} +(-0.0435401 + 0.0365345i) q^{67} +(4.04629 + 0.282124i) q^{69} +(7.01777 + 12.1551i) q^{71} +(4.29405 - 7.43752i) q^{73} +(12.9255 - 9.39492i) q^{75} +(0.802600 + 4.55177i) q^{77} +(-3.50706 - 2.94277i) q^{79} +(5.03875 + 7.45728i) q^{81} +(-5.43304 - 4.55887i) q^{83} +(-0.892053 - 5.05908i) q^{85} +(7.56380 - 5.49775i) q^{87} +(-4.12031 + 7.13659i) q^{89} +(-1.86540 - 3.23097i) q^{91} +(-2.94103 - 0.205061i) q^{93} +(15.6708 - 13.1494i) q^{95} +(2.65109 - 0.964918i) q^{97} +(-18.1336 - 2.54106i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{9}+O(q^{10}) $ 48 * q - 12 * q^9	$ 48 q - 12 q^{9} - 12 q^{17} - 48 q^{21} + 24 q^{25} + 6 q^{29} - 6 q^{33} + 30 q^{37} - 12 q^{41} + 30 q^{45} - 6 q^{49} - 36 q^{53} - 6 q^{57} - 12 q^{61} - 60 q^{65} - 78 q^{69} + 48 q^{73} - 12 q^{77} - 36 q^{81} + 102 q^{85} - 66 q^{89} + 36 q^{93} + 6 q^{97}+O(q^{100}) $ 48 * q - 12 * q^9 - 12 * q^17 - 48 * q^21 + 24 * q^25 + 6 * q^29 - 6 * q^33 + 30 * q^37 - 12 * q^41 + 30 * q^45 - 6 * q^49 - 36 * q^53 - 6 * q^57 - 12 * q^61 - 60 * q^65 - 78 * q^69 + 48 * q^73 - 12 * q^77 - 36 * q^81 + 102 * q^85 - 66 * q^89 + 36 * q^93 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{2}{9}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.418682	−	1.68069i	0.241726	−	0.970344i
$3$	0.418682	−	1.68069i	0.241726	−	0.970344i
$4$		0			0
$5$	3.54422	+	1.28999i	1.58502	+	0.576901i	0.976289	−	0.216473i	$-0.0694552\pi$
$5$	3.54422	+	1.28999i	1.58502	+	0.576901i	0.608735	+	0.793374i	$0.291677\pi$
$6$		0			0
$7$	−0.131496	+	0.745751i	−0.0497008	+	0.281867i	−0.999522	−	0.0309271i	$-0.990154\pi$
$7$	−0.131496	+	0.745751i	−0.0497008	+	0.281867i	0.949821	+	0.312795i	$0.101265\pi$
$8$		0			0
$9$	−2.64941	−	1.40735i	−0.883137	−	0.469116i
$10$		0			0
$11$	5.73551	−	2.08756i	1.72932	−	0.629422i	0.730740	−	0.682656i	$-0.239175\pi$
$11$	5.73551	−	2.08756i	1.72932	−	0.629422i	0.998582	+	0.0532345i	$0.0169531\pi$
$12$		0			0
$13$	−3.77411	+	3.16685i	−1.04675	+	0.878327i	−0.992748	−	0.120214i	$-0.961642\pi$
$13$	−3.77411	+	3.16685i	−1.04675	+	0.878327i	−0.0540011	+	0.998541i	$0.517197\pi$
$14$		0			0
$15$	3.65197	−	5.41662i	0.942935	−	1.39857i
$16$		0			0
$17$	−0.681013	−	1.17955i	−0.165170	−	0.286083i	0.771546	−	0.636174i	$-0.219484\pi$
$17$	−0.681013	−	1.17955i	−0.165170	−	0.286083i	−0.936716	+	0.350091i	$0.886151\pi$
$18$		0			0
$19$	2.71190	−	4.69715i	0.622153	−	1.07760i	−0.366931	−	0.930248i	$-0.619592\pi$
$19$	2.71190	−	4.69715i	0.622153	−	1.07760i	0.989084	−	0.147352i	$-0.0470750\pi$
$20$		0			0
$21$	1.19832	+	0.533236i	0.261494	+	0.116362i
$22$		0			0
$23$	0.406649	+	2.30622i	0.0847921	+	0.480880i	0.997401	+	0.0720467i	$0.0229531\pi$
$23$	0.406649	+	2.30622i	0.0847921	+	0.480880i	−0.912609	+	0.408833i	$0.865936\pi$
$24$		0			0
$25$	7.06720	+	5.93008i	1.41344	+	1.18602i
$26$		0			0
$27$	−3.47457	+	3.86360i	−0.668681	+	0.743549i
$28$		0			0
$29$	4.13561	+	3.47019i	0.767963	+	0.644397i	0.940186	−	0.340661i	$-0.110651\pi$
$29$	4.13561	+	3.47019i	0.767963	+	0.644397i	−0.172224	+	0.985058i	$0.555095\pi$
$30$		0			0
$31$	−0.295571	−	1.67627i	−0.0530862	−	0.301067i	0.946692	−	0.322141i	$-0.104402\pi$
$31$	−0.295571	−	1.67627i	−0.0530862	−	0.301067i	−0.999778	+	0.0210743i	$0.993291\pi$
$32$		0			0
$33$	−1.10717	−	10.5136i	−0.192733	−	1.83019i
$34$		0			0
$35$	−1.42806	+	2.47348i	−0.241387	+	0.418094i
$36$		0			0
$37$	1.11813	+	1.93666i	0.183820	+	0.318385i	0.943178	−	0.332288i	$-0.107820\pi$
$37$	1.11813	+	1.93666i	0.183820	+	0.318385i	−0.759359	+	0.650672i	$0.774487\pi$
$38$		0			0
$39$	3.74233	+	7.66899i	0.599253	+	1.22802i
$40$		0			0
$41$	−1.22528	+	1.02813i	−0.191357	+	0.160567i	−0.733432	−	0.679762i	$-0.762083\pi$
$41$	−1.22528	+	1.02813i	−0.191357	+	0.160567i	0.542076	+	0.840329i	$0.317638\pi$
$42$		0			0
$43$	−5.88030	+	2.14026i	−0.896738	+	0.326386i	−0.748945	−	0.662632i	$-0.769439\pi$
$43$	−5.88030	+	2.14026i	−0.896738	+	0.326386i	−0.147793	+	0.989018i	$0.547217\pi$
$44$		0			0
$45$	−7.57463	−	8.40566i	−1.12916	−	1.25304i
$46$		0			0
$47$	1.93713	−	10.9860i	0.282559	−	1.60247i	−0.431317	−	0.902201i	$-0.641951\pi$
$47$	1.93713	−	10.9860i	0.282559	−	1.60247i	0.713876	−	0.700272i	$-0.246938\pi$
$48$		0			0
$49$	6.03899	+	2.19801i	0.862714	+	0.314002i
$50$		0			0
$51$	−2.26758	+	0.650713i	−0.317525	+	0.0911181i
$52$		0			0
$53$	−7.06071			−0.969864			−0.484932	−	0.874552i	$-0.661156\pi$
$53$	−7.06071			−0.969864			−0.484932	+	0.874552i	$0.661156\pi$
$54$		0			0
$55$	23.0208			3.10413
$56$		0			0
$57$	−6.75901	−	6.52447i	−0.895253	−	0.864187i
$58$		0			0
$59$	−11.6613	−	4.24435i	−1.51817	−	0.552568i	−0.557477	−	0.830192i	$-0.688231\pi$
$59$	−11.6613	−	4.24435i	−1.51817	−	0.552568i	−0.960690	+	0.277625i	$0.910453\pi$
$60$		0			0
$61$	0.963730	−	5.46558i	0.123393	−	0.699796i	−0.858856	−	0.512217i	$-0.828825\pi$
$61$	0.963730	−	5.46558i	0.123393	−	0.699796i	0.982249	−	0.187580i	$-0.0600644\pi$
$62$		0			0
$63$	1.39792	−	1.79074i	0.176121	−	0.225612i
$64$		0			0
$65$	−17.4615	+	6.35546i	−2.16583	+	0.788297i
$66$		0			0
$67$	−0.0435401	+	0.0365345i	−0.00531927	+	0.00446340i	−0.645443	−	0.763808i	$-0.723327\pi$
$67$	−0.0435401	+	0.0365345i	−0.00531927	+	0.00446340i	0.640124	+	0.768272i	$0.278883\pi$
$68$		0			0
$69$	4.04629	+	0.282124i	0.487116	+	0.0339638i
$70$		0			0
$71$	7.01777	+	12.1551i	0.832856	+	1.44255i	0.895764	+	0.444529i	$0.146629\pi$
$71$	7.01777	+	12.1551i	0.832856	+	1.44255i	−0.0629085	+	0.998019i	$0.520038\pi$
$72$		0			0
$73$	4.29405	−	7.43752i	0.502581	−	0.870495i	−0.497415	−	0.867513i	$-0.665717\pi$
$73$	4.29405	−	7.43752i	0.502581	−	0.870495i	0.999996	−	0.00298255i	$-0.000949375\pi$
$74$		0			0
$75$	12.9255	−	9.39492i	1.49251	−	1.08483i
$76$		0			0
$77$	0.802600	+	4.55177i	0.0914647	+	0.518722i
$78$		0			0
$79$	−3.50706	−	2.94277i	−0.394575	−	0.331087i	0.423818	−	0.905748i	$-0.360690\pi$
$79$	−3.50706	−	2.94277i	−0.394575	−	0.331087i	−0.818392	+	0.574660i	$0.805134\pi$
$80$		0			0
$81$	5.03875	+	7.45728i	0.559861	+	0.828586i
$82$		0			0
$83$	−5.43304	−	4.55887i	−0.596354	−	0.500401i	0.293917	−	0.955831i	$-0.405041\pi$
$83$	−5.43304	−	4.55887i	−0.596354	−	0.500401i	−0.890271	+	0.455430i	$0.849485\pi$
$84$		0			0
$85$	−0.892053	−	5.05908i	−0.0967567	−	0.548735i
$86$		0			0
$87$	7.56380	−	5.49775i	0.810924	−	0.589421i
$88$		0			0
$89$	−4.12031	+	7.13659i	−0.436752	+	0.756477i	−0.997437	−	0.0715525i	$-0.977205\pi$
$89$	−4.12031	+	7.13659i	−0.436752	+	0.756477i	0.560685	+	0.828029i	$0.310538\pi$
$90$		0			0
$91$	−1.86540	−	3.23097i	−0.195547	−	0.338698i
$92$		0			0
$93$	−2.94103	−	0.205061i	−0.304971	−	0.0212638i
$94$		0			0
$95$	15.6708	−	13.1494i	1.60780	−	1.34910i
$96$		0			0
$97$	2.65109	−	0.964918i	0.269177	−	0.0979725i	−0.203905	−	0.978991i	$-0.565363\pi$
$97$	2.65109	−	0.964918i	0.269177	−	0.0979725i	0.473083	+	0.881018i	$0.343141\pi$
$98$		0			0
$99$	−18.1336	−	2.54106i	−1.82250	−	0.255386i
$100$		0			0
$101$	0.856502	−	4.85746i	0.0852251	−	0.483336i	−0.912083	−	0.410006i	$-0.865526\pi$
$101$	0.856502	−	4.85746i	0.0852251	−	0.483336i	0.997308	−	0.0733293i	$-0.0233624\pi$
$102$		0			0
$103$	−12.5452	−	4.56609i	−1.23612	−	0.449910i	−0.360429	−	0.932786i	$-0.617370\pi$
$103$	−12.5452	−	4.56609i	−1.23612	−	0.449910i	−0.875689	+	0.482876i	$0.839592\pi$
$104$		0			0
$105$	3.55923	+	3.43573i	0.347346	+	0.335292i
$106$		0			0
$107$	−0.448727			−0.0433801			−0.0216901	−	0.999765i	$-0.506905\pi$
$107$	−0.448727			−0.0433801			−0.0216901	+	0.999765i	$0.506905\pi$
$108$		0			0
$109$	0.841084			0.0805612			0.0402806	−	0.999188i	$-0.487175\pi$
$109$	0.841084			0.0805612			0.0402806	+	0.999188i	$0.487175\pi$
$110$		0			0
$111$	3.72306	−	1.06838i	0.353377	−	0.101406i
$112$		0			0
$113$	−15.7635	−	5.73745i	−1.48291	−	0.539734i	−0.531335	−	0.847162i	$-0.678310\pi$
$113$	−15.7635	−	5.73745i	−1.48291	−	0.539734i	−0.951571	+	0.307428i	$0.900532\pi$
$114$		0			0
$115$	−1.53375	+	8.69832i	−0.143023	+	0.811122i
$116$		0			0
$117$	14.4560	−	3.07881i	1.33646	−	0.284636i
$118$		0			0
$119$	0.969201	−	0.352760i	0.0888465	−	0.0323375i
$120$		0			0
$121$	20.1117	−	16.8757i	1.82834	−	1.53416i
$122$		0			0
$123$	1.21496	+	2.48977i	0.109550	+	0.224495i
$124$		0			0
$125$	7.96875	+	13.8023i	0.712746	+	1.23451i
$126$		0			0
$127$	−2.19489	+	3.80167i	−0.194765	+	0.337343i	−0.946824	−	0.321753i	$-0.895728\pi$
$127$	−2.19489	+	3.80167i	−0.194765	+	0.337343i	0.752058	+	0.659097i	$0.229061\pi$
$128$		0			0
$129$	1.13512	+	10.7790i	0.0999416	+	0.949041i
$130$		0			0
$131$	3.50559	+	19.8812i	0.306284	+	1.73703i	0.617396	+	0.786652i	$0.288187\pi$
$131$	3.50559	+	19.8812i	0.306284	+	1.73703i	−0.311112	+	0.950373i	$0.600701\pi$
$132$		0			0
$133$	3.14630	+	2.64006i	0.272819	+	0.228922i
$134$		0			0
$135$	−17.2986	+	9.21127i	−1.48883	+	0.792780i
$136$		0			0
$137$	8.73272	+	7.32762i	0.746087	+	0.626041i	0.934465	−	0.356056i	$-0.115879\pi$
$137$	8.73272	+	7.32762i	0.746087	+	0.626041i	−0.188378	+	0.982097i	$0.560323\pi$
$138$		0			0
$139$	1.83939	+	10.4317i	0.156015	+	0.884805i	0.957852	+	0.287262i	$0.0927452\pi$
$139$	1.83939	+	10.4317i	0.156015	+	0.884805i	−0.801837	+	0.597543i	$0.796144\pi$
$140$		0			0
$141$	−17.6530	−	7.85535i	−1.48665	−	0.661540i
$142$		0			0
$143$	−15.0355	+	26.0422i	−1.25733	+	2.17776i
$144$		0			0
$145$	10.1810	+	17.6340i	0.845485	+	1.46442i
$146$		0			0
$147$	6.22259	−	9.22938i	0.513231	−	0.761227i
$148$		0			0
$149$	−17.0321	+	14.2916i	−1.39532	+	1.17082i	−0.432193	+	0.901781i	$0.642260\pi$
$149$	−17.0321	+	14.2916i	−1.39532	+	1.17082i	−0.963130	+	0.269035i	$0.913295\pi$
$150$		0			0
$151$	−7.57715	+	2.75786i	−0.616619	+	0.224431i	−0.631397	−	0.775460i	$-0.717518\pi$
$151$	−7.57715	+	2.75786i	−0.616619	+	0.224431i	0.0147777	+	0.999891i	$0.495296\pi$
$152$		0			0
$153$	0.144249	+	4.08353i	0.0116618	+	0.330134i
$154$		0			0
$155$	1.11480	−	6.32235i	0.0895429	−	0.507823i
$156$		0			0
$157$	10.0918	+	3.67311i	0.805411	+	0.293146i	0.711727	−	0.702456i	$-0.247913\pi$
$157$	10.0918	+	3.67311i	0.805411	+	0.293146i	0.0936844	+	0.995602i	$0.470136\pi$
$158$		0			0
$159$	−2.95620	+	11.8668i	−0.234442	+	0.941102i
$160$		0			0
$161$	−1.77334			−0.139759
$162$		0			0
$163$	−14.8288			−1.16148			−0.580742	−	0.814088i	$-0.697237\pi$
$163$	−14.8288			−1.16148			−0.580742	+	0.814088i	$0.697237\pi$
$164$		0			0
$165$	9.63842	−	38.6908i	0.750350	−	3.01207i
$166$		0			0
$167$	3.13082	+	1.13953i	0.242270	+	0.0881791i	0.460302	−	0.887763i	$-0.347741\pi$
$167$	3.13082	+	1.13953i	0.242270	+	0.0881791i	−0.218031	+	0.975942i	$0.569964\pi$
$168$		0			0
$169$	1.95751	−	11.1016i	0.150578	−	0.853968i
$170$		0			0
$171$	−13.7955	+	8.62809i	−1.05496	+	0.659807i
$172$		0			0
$173$	−13.2783	+	4.83289i	−1.00953	+	0.367438i	−0.793251	−	0.608894i	$-0.791613\pi$
$173$	−13.2783	+	4.83289i	−1.00953	+	0.367438i	−0.216276	+	0.976332i	$0.569391\pi$
$174$		0			0
$175$	−5.35167	+	4.49059i	−0.404548	+	0.339456i
$176$		0			0
$177$	−12.0158	+	17.8219i	−0.903162	+	1.33957i
$178$		0			0
$179$	−3.96857	−	6.87376i	−0.296625	−	0.513769i	0.678737	−	0.734382i	$-0.262528\pi$
$179$	−3.96857	−	6.87376i	−0.296625	−	0.513769i	−0.975362	+	0.220612i	$0.929194\pi$
$180$		0			0
$181$	1.83630	−	3.18057i	0.136491	−	0.236410i	−0.789675	−	0.613526i	$-0.789751\pi$
$181$	1.83630	−	3.18057i	0.136491	−	0.236410i	0.926166	+	0.377116i	$0.123084\pi$
$182$		0			0
$183$	−8.78243	−	3.90807i	−0.649216	−	0.288893i
$184$		0			0
$185$	1.46463	+	8.30632i	0.107682	+	0.610693i
$186$		0			0
$187$	−6.36834	−	5.34367i	−0.465699	−	0.390768i
$188$		0			0
$189$	−2.42439	−	3.09921i	−0.176348	−	0.225434i
$190$		0			0
$191$	−10.1440	−	8.51179i	−0.733991	−	0.615891i	0.197226	−	0.980358i	$-0.436807\pi$
$191$	−10.1440	−	8.51179i	−0.733991	−	0.615891i	−0.931216	+	0.364467i	$0.881251\pi$
$192$		0			0
$193$	3.83881	+	21.7710i	0.276324	+	1.56711i	0.734726	+	0.678365i	$0.237311\pi$
$193$	3.83881	+	21.7710i	0.276324	+	1.56711i	−0.458402	+	0.888745i	$0.651578\pi$
$194$		0			0
$195$	3.37072	+	32.0082i	0.241382	+	2.29215i
$196$		0			0
$197$	−5.85620	+	10.1432i	−0.417237	+	0.722676i	−0.995660	−	0.0930608i	$-0.970335\pi$
$197$	−5.85620	+	10.1432i	−0.417237	+	0.722676i	0.578423	+	0.815737i	$0.303668\pi$
$198$		0			0
$199$	8.85330	+	15.3344i	0.627594	+	1.08702i	0.988033	+	0.154242i	$0.0492935\pi$
$199$	8.85330	+	15.3344i	0.627594	+	1.08702i	−0.360439	+	0.932783i	$0.617373\pi$
$200$		0			0
$201$	0.0431735	+	0.0884736i	0.00304523	+	0.00624045i
$202$		0			0
$203$	−3.13171	+	2.62782i	−0.219803	+	0.184437i
$204$		0			0
$205$	−5.66894	+	2.06333i	−0.395936	+	0.144109i
$206$		0			0
$207$	2.16827	−	6.68241i	0.150705	−	0.464460i
$208$		0			0
$209$	5.74858	−	32.6018i	0.397637	−	2.25511i
$210$		0			0
$211$	12.0618	+	4.39015i	0.830371	+	0.302230i	0.722011	−	0.691881i	$-0.243218\pi$
$211$	12.0618	+	4.39015i	0.830371	+	0.302230i	0.108360	+	0.994112i	$0.465440\pi$
$212$		0			0
$213$	23.3672	−	6.70553i	1.60109	−	0.459455i
$214$		0			0
$215$	−23.6020			−1.60964
$216$		0			0
$217$	1.28894			0.0874993
$218$		0			0
$219$	−10.7023	−	10.3309i	−0.723193	−	0.698098i
$220$		0			0
$221$	6.30568	+	2.29508i	0.424166	+	0.154384i
$222$		0			0
$223$	3.44291	−	19.5257i	0.230555	−	1.30754i	−0.621222	−	0.783635i	$-0.713363\pi$
$223$	3.44291	−	19.5257i	0.230555	−	1.30754i	0.851776	−	0.523905i	$-0.175525\pi$
$224$		0			0
$225$	−10.3782	−	25.6572i	−0.691881	−	1.71048i
$226$		0			0
$227$	−16.5863	+	6.03692i	−1.10087	+	0.400685i	−0.827638	−	0.561263i	$-0.810316\pi$
$227$	−16.5863	+	6.03692i	−1.10087	+	0.400685i	−0.273234	+	0.961947i	$0.588093\pi$
$228$		0			0
$229$	−9.59717	+	8.05298i	−0.634199	+	0.532156i	−0.902231	−	0.431254i	$-0.858071\pi$
$229$	−9.59717	+	8.05298i	−0.634199	+	0.532156i	0.268032	+	0.963410i	$0.413627\pi$
$230$		0			0
$231$	7.98613	+	0.556827i	0.525449	+	0.0366365i
$232$		0			0
$233$	−7.26289	−	12.5797i	−0.475808	−	0.824123i	0.523808	−	0.851836i	$-0.324511\pi$
$233$	−7.26289	−	12.5797i	−0.475808	−	0.824123i	−0.999616	+	0.0277130i	$0.991178\pi$
$234$		0			0
$235$	21.0374	−	36.4379i	1.37233	−	2.37695i
$236$		0			0
$237$	−6.41421	+	4.66217i	−0.416648	+	0.302841i
$238$		0			0
$239$	−1.61991	−	9.18695i	−0.104783	−	0.594254i	−0.991307	−	0.131571i	$-0.957998\pi$
$239$	−1.61991	−	9.18695i	−0.104783	−	0.594254i	0.886524	−	0.462683i	$-0.153113\pi$
$240$		0			0
$241$	−6.46851	−	5.42773i	−0.416674	−	0.349631i	0.410222	−	0.911986i	$-0.365451\pi$
$241$	−6.46851	−	5.42773i	−0.416674	−	0.349631i	−0.826896	+	0.562355i	$0.809896\pi$
$242$		0			0
$243$	14.6430	−	5.34633i	0.939347	−	0.342967i
$244$		0			0
$245$	18.5681	+	15.5805i	1.18627	+	0.995401i
$246$		0			0
$247$	4.64017	+	26.3157i	0.295247	+	1.67443i
$248$		0			0
$249$	−9.93674	+	7.22253i	−0.629715	+	0.457709i
$250$		0			0
$251$	5.53198	−	9.58167i	0.349175	−	0.604789i	−0.636928	−	0.770923i	$-0.719795\pi$
$251$	5.53198	−	9.58167i	0.349175	−	0.604789i	0.986103	+	0.166134i	$0.0531284\pi$
$252$		0			0
$253$	7.14670	+	12.3784i	0.449309	+	0.778226i
$254$		0			0
$255$	−8.87622	−	0.618888i	−0.555850	−	0.0387562i
$256$		0			0
$257$	14.2802	−	11.9825i	0.890775	−	0.747449i	−0.0775906	−	0.996985i	$-0.524723\pi$
$257$	14.2802	−	11.9825i	0.890775	−	0.747449i	0.968365	+	0.249536i	$0.0802782\pi$
$258$		0			0
$259$	−1.59130	+	0.579184i	−0.0988783	+	0.0359888i
$260$		0			0
$261$	−6.07316	−	15.0142i	−0.375919	−	0.929354i
$262$		0			0
$263$	0.633193	−	3.59101i	0.0390443	−	0.221431i	−0.959042	−	0.283263i	$-0.908583\pi$
$263$	0.633193	−	3.59101i	0.0390443	−	0.221431i	0.998087	+	0.0618316i	$0.0196942\pi$
$264$		0			0
$265$	−25.0247	−	9.10825i	−1.53726	−	0.559516i
$266$		0			0
$267$	10.2693	+	9.91291i	0.628469	+	0.606660i
$268$		0			0
$269$	22.9765			1.40090			0.700451	−	0.713700i	$-0.252982\pi$
$269$	22.9765			1.40090			0.700451	+	0.713700i	$0.252982\pi$
$270$		0			0
$271$	1.17614			0.0714452			0.0357226	−	0.999362i	$-0.488627\pi$
$271$	1.17614			0.0714452			0.0357226	+	0.999362i	$0.488627\pi$
$272$		0			0
$273$	−6.21126	+	1.78241i	−0.375923	+	0.107876i
$274$		0			0
$275$	52.9134	+	19.2589i	3.19080	+	1.16135i
$276$		0			0
$277$	−4.70779	+	26.6992i	−0.282864	+	1.60420i	0.429954	+	0.902851i	$0.358530\pi$
$277$	−4.70779	+	26.6992i	−0.282864	+	1.60420i	−0.712818	+	0.701349i	$0.752581\pi$
$278$		0			0
$279$	−1.57600	+	4.85709i	−0.0943527	+	0.290787i
$280$		0			0
$281$	−8.54284	+	3.10934i	−0.509623	+	0.185488i	−0.584017	−	0.811741i	$-0.698520\pi$
$281$	−8.54284	+	3.10934i	−0.509623	+	0.185488i	0.0743941	+	0.997229i	$0.476298\pi$
$282$		0			0
$283$	−22.8426	+	19.1672i	−1.35785	+	1.13937i	−0.381212	+	0.924488i	$0.624493\pi$
$283$	−22.8426	+	19.1672i	−1.35785	+	1.13937i	−0.976639	+	0.214885i	$0.931062\pi$
$284$		0			0
$285$	−15.5389	−	31.8432i	−0.920446	−	1.88623i
$286$		0			0
$287$	−0.605611	−	1.04895i	−0.0357481	−	0.0619175i
$288$		0			0
$289$	7.57244	−	13.1159i	0.445438	−	0.771521i
$290$		0			0
$291$	−0.511759	−	4.85964i	−0.0299999	−	0.284877i
$292$		0			0
$293$	−1.31227	−	7.44227i	−0.0766638	−	0.434782i	−0.998846	−	0.0480266i	$-0.984707\pi$
$293$	−1.31227	−	7.44227i	−0.0766638	−	0.434782i	0.922182	−	0.386756i	$-0.126404\pi$
$294$		0			0
$295$	−35.8549	−	30.0858i	−2.08755	−	1.75166i
$296$		0			0
$297$	−11.8630	+	29.4131i	−0.688359	+	1.70672i
$298$		0			0
$299$	−8.83819	−	7.41612i	−0.511126	−	0.428885i
$300$		0			0
$301$	−0.822861	−	4.66668i	−0.0474289	−	0.268983i
$302$		0			0
$303$	−7.80527	−	3.47324i	−0.448401	−	0.199533i
$304$		0			0
$305$	10.4662	−	18.1280i	0.599294	−	1.03801i
$306$		0			0
$307$	−2.38378	−	4.12882i	−0.136049	−	0.235644i	0.789948	−	0.613173i	$-0.210107\pi$
$307$	−2.38378	−	4.12882i	−0.136049	−	0.235644i	−0.925998	+	0.377529i	$0.876774\pi$
$308$		0			0
$309$	−12.9266	+	19.1728i	−0.735370	+	1.09071i
$310$		0			0
$311$	1.37651	−	1.15503i	0.0780546	−	0.0654955i	−0.602926	−	0.797797i	$-0.705998\pi$
$311$	1.37651	−	1.15503i	0.0780546	−	0.0654955i	0.680980	+	0.732302i	$0.261554\pi$
$312$		0			0
$313$	14.7155	−	5.35600i	0.831768	−	0.302739i	0.109184	−	0.994022i	$-0.465176\pi$
$313$	14.7155	−	5.35600i	0.831768	−	0.302739i	0.722584	+	0.691283i	$0.242954\pi$
$314$		0			0
$315$	7.26456	−	4.54348i	0.409312	−	0.255996i
$316$		0			0
$317$	−2.98393	+	16.9227i	−0.167594	+	0.950475i	0.778755	+	0.627328i	$0.215852\pi$
$317$	−2.98393	+	16.9227i	−0.167594	+	0.950475i	−0.946349	+	0.323146i	$0.895259\pi$
$318$		0			0
$319$	30.9640	+	11.2700i	1.73365	+	0.630998i
$320$		0			0
$321$	−0.187874	+	0.754170i	−0.0104861	+	0.0420937i
$322$		0			0
$323$	−7.38736			−0.411044
$324$		0			0
$325$	−45.4520			−2.52123
$326$		0			0
$327$	0.352147	−	1.41360i	0.0194738	−	0.0781721i
$328$		0			0
$329$	7.93810	+	2.88923i	0.437641	+	0.159288i
$330$		0			0
$331$	4.31231	−	24.4563i	0.237026	−	1.34424i	−0.601280	−	0.799039i	$-0.705342\pi$
$331$	4.31231	−	24.4563i	0.237026	−	1.34424i	0.838305	−	0.545201i	$-0.183547\pi$
$332$		0			0
$333$	−0.236836	−	6.70460i	−0.0129786	−	0.367410i
$334$		0			0
$335$	−0.201445	+	0.0733199i	−0.0110061	+	0.00400590i
$336$		0			0
$337$	−2.33704	+	1.96101i	−0.127307	+	0.106823i	−0.704218	−	0.709984i	$-0.748702\pi$
$337$	−2.33704	+	1.96101i	−0.127307	+	0.106823i	0.576911	+	0.816807i	$0.304258\pi$
$338$		0			0
$339$	−16.2428	+	24.0913i	−0.882185	+	1.30846i
$340$		0			0
$341$	−5.19455	−	8.99723i	−0.281301	−	0.487227i
$342$		0			0
$343$	−5.08367	+	8.80517i	−0.274492	+	0.475435i
$344$		0			0
$345$	13.9770	+	6.21958i	0.752496	+	0.334851i
$346$		0			0
$347$	1.86707	+	10.5887i	0.100230	+	0.568430i	0.993019	+	0.117956i	$0.0376341\pi$
$347$	1.86707	+	10.5887i	0.100230	+	0.568430i	−0.892789	+	0.450475i	$0.851255\pi$
$348$		0			0
$349$	−4.19338	−	3.51866i	−0.224466	−	0.188350i	0.523618	−	0.851953i	$-0.324582\pi$
$349$	−4.19338	−	3.51866i	−0.224466	−	0.188350i	−0.748085	+	0.663603i	$0.769026\pi$
$350$		0			0
$351$	0.877959	−	25.5851i	0.0468620	−	1.36563i
$352$		0			0
$353$	11.7248	+	9.83828i	0.624048	+	0.523639i	0.899073	−	0.437798i	$-0.144242\pi$
$353$	11.7248	+	9.83828i	0.624048	+	0.523639i	−0.275025	+	0.961437i	$0.588686\pi$
$354$		0			0
$355$	9.19251	+	52.1333i	0.487888	+	2.76695i
$356$		0			0
$357$	−0.187092	−	1.77662i	−0.00990196	−	0.0940285i
$358$		0			0
$359$	−1.52051	+	2.63360i	−0.0802495	+	0.138996i	−0.903357	−	0.428889i	$-0.858905\pi$
$359$	−1.52051	+	2.63360i	−0.0802495	+	0.138996i	0.823108	+	0.567886i	$0.192238\pi$
$360$		0			0
$361$	−5.20881	−	9.02192i	−0.274148	−	0.474838i
$362$		0			0
$363$	−19.9424	−	40.8670i	−1.04670	−	2.14496i
$364$		0			0
$365$	24.8134	−	20.8209i	1.29879	−	1.08982i
$366$		0			0
$367$	−17.5175	+	6.37584i	−0.914405	+	0.332816i	−0.756010	−	0.654560i	$-0.772854\pi$
$367$	−17.5175	+	6.37584i	−0.914405	+	0.332816i	−0.158395	+	0.987376i	$0.550632\pi$
$368$		0			0
$369$	4.69321	−	0.999550i	0.244319	−	0.0520345i
$370$		0			0
$371$	0.928456	−	5.26553i	0.0482030	−	0.273373i
$372$		0			0
$373$	14.9410	+	5.43807i	0.773614	+	0.281572i	0.698507	−	0.715603i	$-0.253848\pi$
$373$	14.9410	+	5.43807i	0.773614	+	0.281572i	0.0751067	+	0.997176i	$0.476070\pi$
$374$		0			0
$375$	26.5337	−	7.61419i	1.37019	−	0.393195i
$376$		0			0
$377$	−26.5978			−1.36986
$378$		0			0
$379$	11.0920			0.569759			0.284879	−	0.958563i	$-0.408046\pi$
$379$	11.0920			0.569759			0.284879	+	0.958563i	$0.408046\pi$
$380$		0			0
$381$	5.47044	+	5.28062i	0.280259	+	0.270534i
$382$		0			0
$383$	31.4979	+	11.4643i	1.60947	+	0.585799i	0.981335	−	0.192307i	$-0.0615969\pi$
$383$	31.4979	+	11.4643i	1.60947	+	0.585799i	0.628134	+	0.778106i	$0.283819\pi$
$384$		0			0
$385$	−3.02715	+	17.1678i	−0.154278	+	0.874953i
$386$		0			0
$387$	18.5914	+	2.60521i	0.945055	+	0.132430i
$388$		0			0
$389$	−10.7824	+	3.92446i	−0.546688	+	0.198978i	−0.600574	−	0.799569i	$-0.705061\pi$
$389$	−10.7824	+	3.92446i	−0.546688	+	0.198978i	0.0538862	+	0.998547i	$0.482839\pi$
$390$		0			0
$391$	2.44337	−	2.05023i	0.123566	−	0.103684i
$392$		0			0
$393$	34.8817	+	2.43210i	1.75955	+	0.122683i
$394$		0			0
$395$	−8.63363	−	14.9539i	−0.434405	−	0.752412i
$396$		0			0
$397$	14.2066	−	24.6065i	0.713008	−	1.23497i	−0.250715	−	0.968061i	$-0.580666\pi$
$397$	14.2066	−	24.6065i	0.713008	−	1.23497i	0.963723	−	0.266905i	$-0.0860010\pi$
$398$		0			0
$399$	5.75441	−	4.18260i	0.288081	−	0.209392i
$400$		0			0
$401$	−2.30214	−	13.0561i	−0.114963	−	0.651989i	−0.986768	−	0.162136i	$-0.948162\pi$
$401$	−2.30214	−	13.0561i	−0.114963	−	0.651989i	0.871805	−	0.489853i	$-0.162950\pi$
$402$		0			0
$403$	6.42401	+	5.39038i	0.320003	+	0.268514i
$404$		0			0
$405$	8.23862	+	32.9302i	0.409380	+	1.63631i
$406$		0			0
$407$	10.4559	+	8.77357i	0.518281	+	0.434890i
$408$		0			0
$409$	0.539392	+	3.05905i	0.0266712	+	0.151260i	0.995235	−	0.0975053i	$-0.0310863\pi$
$409$	0.539392	+	3.05905i	0.0266712	+	0.151260i	−0.968564	+	0.248765i	$0.919975\pi$
$410$		0			0
$411$	15.9717	−	11.6090i	0.787824	−	0.572630i
$412$		0			0
$413$	4.69864	−	8.13828i	0.231205	−	0.400459i
$414$		0			0
$415$	−13.3750	−	23.1662i	−0.656553	−	1.13718i
$416$		0			0
$417$	18.3025	+	1.27613i	0.896279	+	0.0624924i
$418$		0			0
$419$	14.9118	−	12.5125i	0.728489	−	0.611275i	−0.201230	−	0.979544i	$-0.564494\pi$
$419$	14.9118	−	12.5125i	0.728489	−	0.611275i	0.929719	+	0.368269i	$0.120050\pi$
$420$		0			0
$421$	3.33484	−	1.21378i	0.162530	−	0.0591562i	−0.259474	−	0.965750i	$-0.583549\pi$
$421$	3.33484	−	1.21378i	0.162530	−	0.0591562i	0.422004	+	0.906594i	$0.361327\pi$
$422$		0			0
$423$	−20.5934	+	26.3802i	−1.00128	+	1.28265i
$424$		0			0
$425$	2.18197	−	12.3746i	0.105841	−	0.600255i
$426$		0			0
$427$	3.94924	+	1.43741i	0.191117	+	0.0695609i
$428$		0			0
$429$	37.4736	+	36.1733i	1.80924	+	1.74646i
$430$		0			0
$431$	−28.0507			−1.35116			−0.675578	−	0.737289i	$-0.736106\pi$
$431$	−28.0507			−1.35116			−0.675578	+	0.737289i	$0.736106\pi$
$432$		0			0
$433$	−2.13469			−0.102587			−0.0512934	−	0.998684i	$-0.516334\pi$
$433$	−2.13469			−0.102587			−0.0512934	+	0.998684i	$0.516334\pi$
$434$		0			0
$435$	33.8998	−	9.72801i	1.62537	−	0.466422i
$436$		0			0
$437$	11.9354	+	4.34415i	0.570950	+	0.207809i
$438$		0			0
$439$	1.21930	−	6.91501i	0.0581941	−	0.330035i	−0.941787	−	0.336211i	$-0.890855\pi$
$439$	1.21930	−	6.91501i	0.0581941	−	0.330035i	0.999981	+	0.00617535i	$0.00196569\pi$
$440$		0			0
$441$	−12.9064	−	14.3224i	−0.614591	−	0.682019i
$442$		0			0
$443$	−4.38192	+	1.59489i	−0.208191	+	0.0757755i	−0.444011	−	0.896021i	$-0.646445\pi$
$443$	−4.38192	+	1.59489i	−0.208191	+	0.0757755i	0.235819	+	0.971797i	$0.424223\pi$
$444$		0			0
$445$	−23.8094	+	19.9785i	−1.12867	+	0.947071i
$446$		0			0
$447$	16.8887	+	34.6093i	0.798808	+	1.63696i
$448$		0			0
$449$	5.11368	+	8.85715i	0.241329	+	0.417995i	0.961093	−	0.276224i	$-0.0890832\pi$
$449$	5.11368	+	8.85715i	0.241329	+	0.417995i	−0.719764	+	0.694219i	$0.755750\pi$
$450$		0			0
$451$	−4.88132	+	8.45470i	−0.229853	+	0.398116i
$452$		0			0
$453$	1.46267	+	13.8895i	0.0687224	+	0.652584i
$454$		0			0
$455$	−2.44347	−	13.8576i	−0.114552	−	0.649656i
$456$		0			0
$457$	1.58906	+	1.33338i	0.0743329	+	0.0623727i	0.679197	−	0.733956i	$-0.262328\pi$
$457$	1.58906	+	1.33338i	0.0743329	+	0.0623727i	−0.604864	+	0.796329i	$0.706773\pi$
$458$		0			0
$459$	6.92353	+	1.46727i	0.323163	+	0.0684861i
$460$		0			0
$461$	−15.5664	−	13.0617i	−0.724998	−	0.608345i	0.203765	−	0.979020i	$-0.434682\pi$
$461$	−15.5664	−	13.0617i	−0.724998	−	0.608345i	−0.928763	+	0.370675i	$0.879127\pi$
$462$		0			0
$463$	−5.65224	−	32.0554i	−0.262682	−	1.48974i	−0.775556	−	0.631279i	$-0.782530\pi$
$463$	−5.65224	−	32.0554i	−0.262682	−	1.48974i	0.512874	−	0.858464i	$-0.328581\pi$
$464$		0			0
$465$	−10.1591	−	4.52068i	−0.471118	−	0.209642i
$466$		0			0
$467$	−0.641936	+	1.11187i	−0.0297052	+	0.0514510i	−0.880496	−	0.474054i	$-0.842790\pi$
$467$	−0.641936	+	1.11187i	−0.0297052	+	0.0514510i	0.850791	+	0.525505i	$0.176124\pi$
$468$		0			0
$469$	−0.0215203	−	0.0372742i	−0.000993714	−	0.00172116i
$470$		0			0
$471$	10.3986	−	15.4232i	0.479142	−	0.710665i
$472$		0			0
$473$	−29.2586	+	24.5509i	−1.34531	+	1.12885i
$474$		0			0
$475$	47.0200	−	17.1139i	2.15743	−	0.785239i
$476$		0			0
$477$	18.7067	+	9.93687i	0.856522	+	0.454978i
$478$		0			0
$479$	1.87172	−	10.6151i	0.0855211	−	0.485014i	−0.911722	−	0.410808i	$-0.865247\pi$
$479$	1.87172	−	10.6151i	0.0855211	−	0.485014i	0.997243	−	0.0742062i	$-0.0236423\pi$
$480$		0			0
$481$	−10.3531	−	3.76821i	−0.472059	−	0.171815i
$482$		0			0
$483$	−0.742465	+	2.98042i	−0.0337833	+	0.135614i
$484$		0			0
$485$	10.6408			0.483173
$486$		0			0
$487$	23.7182			1.07477			0.537387	−	0.843336i	$-0.319412\pi$
$487$	23.7182			1.07477			0.537387	+	0.843336i	$0.319412\pi$
$488$		0			0
$489$	−6.20857	+	24.9226i	−0.280761	+	1.12704i
$490$		0			0
$491$	31.5174	+	11.4714i	1.42236	+	0.517697i	0.934732	−	0.355353i	$-0.115639\pi$
$491$	31.5174	+	11.4714i	1.42236	+	0.517697i	0.487630	+	0.873051i	$0.337862\pi$
$492$		0			0
$493$	1.27685	−	7.24140i	0.0575066	−	0.326136i
$494$		0			0
$495$	−60.9916	−	32.3983i	−2.74137	−	1.45620i
$496$		0			0
$497$	−9.98751	+	3.63516i	−0.448001	+	0.163059i
$498$		0			0
$499$	15.1104	−	12.6792i	0.676436	−	0.567597i	−0.238526	−	0.971136i	$-0.576664\pi$
$499$	15.1104	−	12.6792i	0.676436	−	0.567597i	0.914963	+	0.403539i	$0.132220\pi$
$500$		0			0
$501$	3.22600	−	4.78483i	0.144127	−	0.213770i
$502$		0			0
$503$	−5.73943	−	9.94098i	−0.255908	−	0.443246i	0.709233	−	0.704974i	$-0.249041\pi$
$503$	−5.73943	−	9.94098i	−0.255908	−	0.443246i	−0.965142	+	0.261727i	$0.915708\pi$
$504$		0			0
$505$	9.30171	−	16.1110i	0.413921	−	0.716932i
$506$		0			0
$507$	−17.8387	−	7.93799i	−0.792244	−	0.352539i
$508$		0			0
$509$	−1.09394	−	6.20404i	−0.0484880	−	0.274989i	0.950918	−	0.309442i	$-0.100142\pi$
$509$	−1.09394	−	6.20404i	−0.0484880	−	0.274989i	−0.999406	+	0.0344529i	$0.989031\pi$
$510$		0			0
$511$	4.98188	+	4.18030i	0.220386	+	0.184925i
$512$		0			0
$513$	8.72520	+	26.7983i	0.385227	+	1.18317i
$514$		0			0
$515$	−38.5728	−	32.3664i	−1.69972	−	1.42624i
$516$		0			0
$517$	−11.8235	−	67.0542i	−0.519995	−	2.94904i
$518$		0			0
$519$	2.56320	+	24.3400i	0.112512	+	1.06841i
$520$		0			0
$521$	−0.489360	+	0.847596i	−0.0214392	+	0.0371339i	−0.876546	−	0.481318i	$-0.840158\pi$
$521$	−0.489360	+	0.847596i	−0.0214392	+	0.0371339i	0.855107	+	0.518452i	$0.173492\pi$
$522$		0			0
$523$	0.982832	+	1.70231i	0.0429762	+	0.0744370i	0.886713	−	0.462320i	$-0.152983\pi$
$523$	0.982832	+	1.70231i	0.0429762	+	0.0744370i	−0.843737	+	0.536757i	$0.819649\pi$
$524$		0			0
$525$	5.30662	+	10.8746i	0.231600	+	0.474607i
$526$		0			0
$527$	−1.77595	+	1.49020i	−0.0773617	+	0.0649142i
$528$		0			0
$529$	16.4596	−	5.99082i	0.715637	−	0.260471i
$530$		0			0
$531$	24.9222	+	27.6565i	1.08153	+	1.20019i
$532$		0			0
$533$	1.36840	−	7.76056i	0.0592718	−	0.336147i
$534$		0			0
$535$	−1.59039	−	0.578854i	−0.0687585	−	0.0250260i
$536$		0			0
$537$	−13.2142	+	3.79200i	−0.570235	+	0.163637i
$538$		0			0
$539$	39.2252			1.68955
$540$		0			0
$541$	−30.0616			−1.29245			−0.646224	−	0.763148i	$-0.723653\pi$
$541$	−30.0616			−1.29245			−0.646224	+	0.763148i	$0.723653\pi$
$542$		0			0
$543$	−4.57672	−	4.41790i	−0.196406	−	0.189590i
$544$		0			0
$545$	2.98098	+	1.08499i	0.127691	+	0.0464759i
$546$		0			0
$547$	5.39179	−	30.5784i	0.230536	−	1.30744i	−0.621277	−	0.783591i	$-0.713386\pi$
$547$	5.39179	−	30.5784i	0.230536	−	1.30744i	0.851814	−	0.523845i	$-0.175503\pi$
$548$		0			0
$549$	−10.2453	+	13.1243i	−0.437258	+	0.560130i
$550$		0			0
$551$	27.5153	−	10.0148i	1.17219	−	0.426643i
$552$		0			0
$553$	2.65574	−	2.22843i	0.112933	−	0.0947624i
$554$		0			0
$555$	14.5735	+	1.01613i	0.618612	+	0.0431323i
$556$		0			0
$557$	−11.7981	−	20.4349i	−0.499901	−	0.865853i	0.500099	−	0.865968i	$-0.333297\pi$
$557$	−11.7981	−	20.4349i	−0.499901	−	0.865853i	−1.00000		0.000114624i	$0.999964\pi$
$558$		0			0
$559$	15.4150	−	26.6996i	0.651986	−	1.12927i
$560$		0			0
$561$	−11.6473	+	8.46587i	−0.491751	+	0.357429i
$562$		0			0
$563$	−2.18201	−	12.3748i	−0.0919607	−	0.521535i	−0.995636	−	0.0933176i	$-0.970253\pi$
$563$	−2.18201	−	12.3748i	−0.0919607	−	0.521535i	0.903676	−	0.428218i	$-0.140858\pi$
$564$		0			0
$565$	−48.4681	−	40.6696i	−2.03907	−	1.71098i
$566$		0			0
$567$	−6.22385	+	2.77705i	−0.261377	+	0.116625i
$568$		0			0
$569$	−10.1660	−	8.53027i	−0.426180	−	0.357607i	0.404328	−	0.914614i	$-0.367505\pi$
$569$	−10.1660	−	8.53027i	−0.426180	−	0.357607i	−0.830508	+	0.557007i	$0.811950\pi$
$570$		0			0
$571$	0.322923	+	1.83139i	0.0135139	+	0.0766413i	0.990819	−	0.135196i	$-0.0431664\pi$
$571$	0.322923	+	1.83139i	0.0135139	+	0.0766413i	−0.977305	+	0.211837i	$0.932055\pi$
$572$		0			0
$573$	−18.5527	+	13.4851i	−0.775051	+	0.563347i
$574$		0			0
$575$	−10.8022	+	18.7100i	−0.450483	+	0.780259i
$576$		0			0
$577$	20.3491	+	35.2457i	0.847144	+	1.46730i	0.883747	+	0.467966i	$0.155013\pi$
$577$	20.3491	+	35.2457i	0.847144	+	1.46730i	−0.0366031	+	0.999330i	$0.511654\pi$
$578$		0			0
$579$	38.1974	+	2.66329i	1.58743	+	0.110682i
$580$		0			0
$581$	4.11420	−	3.45223i	0.170686	−	0.143222i
$582$		0			0
$583$	−40.4968	+	14.7396i	−1.67721	+	0.610453i
$584$		0			0
$585$	55.2069	+	7.73613i	2.28253	+	0.319850i
$586$		0			0
$587$	3.89189	−	22.0720i	0.160635	−	0.911009i	−0.792816	−	0.609462i	$-0.791386\pi$
$587$	3.89189	−	22.0720i	0.160635	−	0.911009i	0.953451	−	0.301548i	$-0.0975032\pi$
$588$		0			0
$589$	−8.67524	−	3.15753i	−0.357457	−	0.130104i
$590$		0			0
$591$	14.5957	+	14.0892i	0.600387	+	0.579554i
$592$		0			0
$593$	19.7576			0.811349			0.405675	−	0.914018i	$-0.367037\pi$
$593$	19.7576			0.811349			0.405675	+	0.914018i	$0.367037\pi$
$594$		0			0
$595$	3.89012			0.159479
$596$		0			0
$597$	29.4790	−	8.45939i	1.20649	−	0.346220i
$598$		0			0
$599$	−13.6712	−	4.97589i	−0.558588	−	0.203309i	0.0472699	−	0.998882i	$-0.484948\pi$
$599$	−13.6712	−	4.97589i	−0.558588	−	0.203309i	−0.605858	+	0.795573i	$0.707170\pi$
$600$		0			0
$601$	1.52276	−	8.63602i	0.0621148	−	0.352271i	−0.937871	−	0.346984i	$-0.887206\pi$
$601$	1.52276	−	8.63602i	0.0621148	−	0.352271i	0.999986	−	0.00528712i	$-0.00168295\pi$
$602$		0			0
$603$	0.166772	−	0.0355188i	0.00679149	−	0.00144644i
$604$		0			0
$605$	93.0499	−	33.8674i	3.78302	−	1.37690i
$606$		0			0
$607$	10.6199	−	8.91116i	0.431049	−	0.361693i	−0.401299	−	0.915947i	$-0.631441\pi$
$607$	10.6199	−	8.91116i	0.431049	−	0.361693i	0.832347	+	0.554255i	$0.186997\pi$
$608$		0			0
$609$	3.10534	+	6.36364i	0.125835	+	0.257868i
$610$		0			0
$611$	27.4801	+	47.5969i	1.11173	+	1.92557i
$612$		0			0
$613$	−2.76181	+	4.78360i	−0.111549	+	0.193208i	−0.916395	−	0.400276i	$-0.868914\pi$
$613$	−2.76181	+	4.78360i	−0.111549	+	0.193208i	0.804846	+	0.593483i	$0.202248\pi$
$614$		0			0
$615$	1.09432	+	10.3916i	0.0441271	+	0.419029i
$616$		0			0
$617$	−3.98861	−	22.6205i	−0.160575	−	0.910668i	−0.953510	−	0.301361i	$-0.902559\pi$
$617$	−3.98861	−	22.6205i	−0.160575	−	0.910668i	0.792935	−	0.609307i	$-0.208552\pi$
$618$		0			0
$619$	−16.5990	−	13.9282i	−0.667171	−	0.559823i	0.245056	−	0.969509i	$-0.421194\pi$
$619$	−16.5990	−	13.9282i	−0.667171	−	0.559823i	−0.912226	+	0.409686i	$0.865638\pi$
$620$		0			0
$621$	−10.3232	−	6.44199i	−0.414257	−	0.258508i
$622$		0			0
$623$	−4.78031	−	4.01116i	−0.191519	−	0.160704i
$624$		0			0
$625$	2.42817	+	13.7708i	0.0971268	+	0.550833i
$626$		0			0
$627$	−52.3866	−	23.3113i	−2.09212	−	0.930965i
$628$		0			0
$629$	1.52292	−	2.63778i	0.0607230	−	0.105175i
$630$		0			0
$631$	19.2624	+	33.3634i	0.766824	+	1.32818i	0.939277	+	0.343160i	$0.111497\pi$
$631$	19.2624	+	33.3634i	0.766824	+	1.32818i	−0.172453	+	0.985018i	$0.555169\pi$
$632$		0			0
$633$	12.4285	−	18.4341i	0.493990	−	0.732689i
$634$		0			0
$635$	−12.6833	+	10.6425i	−0.503321	+	0.422337i
$636$		0			0
$637$	−29.7526	+	10.8291i	−1.17884	+	0.429063i
$638$		0			0
$639$	−1.48647	−	42.0804i	−0.0588037	−	1.66467i
$640$		0			0
$641$	3.82869	−	21.7136i	0.151224	−	0.857635i	−0.810933	−	0.585139i	$-0.801040\pi$
$641$	3.82869	−	21.7136i	0.151224	−	0.857635i	0.962157	−	0.272496i	$-0.0878490\pi$
$642$		0			0
$643$	−21.6302	−	7.87273i	−0.853010	−	0.310470i	−0.121743	−	0.992562i	$-0.538848\pi$
$643$	−21.6302	−	7.87273i	−0.853010	−	0.310470i	−0.731267	+	0.682091i	$0.761071\pi$
$644$		0			0
$645$	−9.88174	+	39.6675i	−0.389093	+	1.56191i
$646$		0			0
$647$	2.78966			0.109673			0.0548364	−	0.998495i	$-0.482536\pi$
$647$	2.78966			0.109673			0.0548364	+	0.998495i	$0.482536\pi$
$648$		0			0
$649$	−75.7436			−2.97320
$650$		0			0
$651$	0.539658	−	2.16631i	0.0211509	−	0.0849044i
$652$		0			0
$653$	−18.7331	−	6.81830i	−0.733084	−	0.266821i	−0.0516142	−	0.998667i	$-0.516437\pi$
$653$	−18.7331	−	6.81830i	−0.733084	−	0.266821i	−0.681470	+	0.731846i	$0.738659\pi$
$654$		0			0
$655$	−13.2219	+	74.9854i	−0.516624	+	2.92992i
$656$		0			0
$657$	−21.8439	+	13.6618i	−0.852210	+	0.532998i
$658$		0			0
$659$	−32.7420	+	11.9171i	−1.27545	+	0.464225i	−0.888924	−	0.458055i	$-0.848546\pi$
$659$	−32.7420	+	11.9171i	−1.27545	+	0.464225i	−0.386523	+	0.922280i	$0.626324\pi$
$660$		0			0
$661$	−13.2676	+	11.1328i	−0.516050	+	0.433017i	−0.863252	−	0.504773i	$-0.831576\pi$
$661$	−13.2676	+	11.1328i	−0.516050	+	0.433017i	0.347202	+	0.937790i	$0.387132\pi$
$662$		0			0
$663$	6.49738	−	9.63695i	0.252337	−	0.374268i
$664$		0			0
$665$	7.74553	+	13.4156i	0.300359	+	0.520237i
$666$		0			0
$667$	−6.32127	+	10.9488i	−0.244760	+	0.423938i
$668$		0			0
$669$	−31.3751	−	13.9615i	−1.21303	−	0.539784i
$670$		0			0
$671$	−5.88223	−	33.3598i	−0.227081	−	1.28784i
$672$		0			0
$673$	−11.3975	−	9.56360i	−0.439340	−	0.368650i	0.396122	−	0.918198i	$-0.370356\pi$
$673$	−11.3975	−	9.56360i	−0.439340	−	0.368650i	−0.835462	+	0.549548i	$0.814800\pi$
$674$		0			0
$675$	−47.4669	+	6.70031i	−1.82700	+	0.257895i
$676$		0			0
$677$	−32.9472	−	27.6460i	−1.26626	−	1.06252i	−0.994985	−	0.100019i	$-0.968109\pi$
$677$	−32.9472	−	27.6460i	−1.26626	−	1.06252i	−0.271277	−	0.962501i	$-0.587446\pi$
$678$		0			0
$679$	0.370981	+	2.10394i	0.0142369	+	0.0807416i
$680$		0			0
$681$	3.20178	+	30.4039i	0.122692	+	1.16508i
$682$		0			0
$683$	−21.4045	+	37.0737i	−0.819020	+	1.41858i	0.0873850	+	0.996175i	$0.472149\pi$
$683$	−21.4045	+	37.0737i	−0.819020	+	1.41858i	−0.906405	+	0.422410i	$0.861184\pi$
$684$		0			0
$685$	21.4981	+	37.2358i	0.821401	+	1.42271i
$686$		0			0
$687$	9.51637	+	19.5015i	0.363072	+	0.744028i
$688$		0			0
$689$	26.6479	−	22.3602i	1.01520	−	0.851857i
$690$		0			0
$691$	−13.4912	+	4.91038i	−0.513228	+	0.186800i	−0.585634	−	0.810576i	$-0.699154\pi$
$691$	−13.4912	+	4.91038i	−0.513228	+	0.186800i	0.0724062	+	0.997375i	$0.476932\pi$
$692$		0			0
$693$	4.27950	−	13.1890i	0.162565	−	0.501010i
$694$		0			0
$695$	−6.93759	+	39.3450i	−0.263158	+	1.49244i
$696$		0			0
$697$	2.04716	+	0.745107i	0.0775419	+	0.0282229i
$698$		0			0
$699$	−24.1834	+	6.93974i	−0.914699	+	0.262485i
$700$		0			0
$701$	−19.3349			−0.730271			−0.365135	−	0.930954i	$-0.618977\pi$
$701$	−19.3349			−0.730271			−0.365135	+	0.930954i	$0.618977\pi$
$702$		0			0
$703$	12.1290			0.457455
$704$		0			0
$705$	−52.4327	−	50.6132i	−1.97473	−	1.90621i
$706$		0			0
$707$	3.50983	+	1.27747i	0.132001	+	0.0480444i
$708$		0			0
$709$	7.49170	−	42.4875i	0.281357	−	1.59565i	−0.436660	−	0.899627i	$-0.643839\pi$
$709$	7.49170	−	42.4875i	0.281357	−	1.59565i	0.718016	−	0.696026i	$-0.245050\pi$
$710$		0			0
$711$	5.15013	+	12.7322i	0.193145	+	0.477497i
$712$		0			0
$713$	3.74565	−	1.36330i	0.140276	−	0.0510561i
$714$		0			0
$715$	−86.8831	+	72.9036i	−3.24924	+	2.72644i
$716$		0			0
$717$	−16.1186	−	1.12386i	−0.601960	−	0.0419712i
$718$		0			0
$719$	15.5960	+	27.0131i	0.581633	+	1.00742i	0.995286	+	0.0969829i	$0.0309192\pi$
$719$	15.5960	+	27.0131i	0.581633	+	1.00742i	−0.413653	+	0.910434i	$0.635747\pi$
$720$		0			0
$721$	5.05481	−	8.75519i	0.188251	−	0.326060i
$722$		0			0
$723$	−11.8306	+	8.59905i	−0.439983	+	0.319802i
$724$		0			0
$725$	8.64865	+	49.0490i	0.321203	+	1.82163i
$726$		0			0
$727$	1.66573	+	1.39772i	0.0617786	+	0.0518384i	0.673154	−	0.739502i	$-0.264939\pi$
$727$	1.66573	+	1.39772i	0.0617786	+	0.0518384i	−0.611376	+	0.791341i	$0.709383\pi$
$728$		0			0
$729$	−2.85474	−	26.8487i	−0.105731	−	0.994395i
$730$		0			0
$731$	6.52910	+	5.47857i	0.241488	+	0.202632i
$732$		0			0
$733$	6.98610	+	39.6202i	0.258038	+	1.46340i	0.788153	+	0.615479i	$0.211037\pi$
$733$	6.98610	+	39.6202i	0.258038	+	1.46340i	−0.530116	+	0.847925i	$0.677852\pi$
$734$		0			0
$735$	33.9600	−	24.6839i	1.25264	−	0.910479i
$736$		0			0
$737$	−0.173457	+	0.300436i	−0.00638937	+	0.0110667i
$738$		0			0
$739$	−15.7816	−	27.3345i	−0.580535	−	1.00552i	−0.995416	−	0.0956404i	$-0.969510\pi$
$739$	−15.7816	−	27.3345i	−0.580535	−	1.00552i	0.414881	−	0.909876i	$-0.363823\pi$
$740$		0			0
$741$	46.1712	+	3.21926i	1.69614	+	0.118262i
$742$		0			0
$743$	−23.1476	+	19.4231i	−0.849203	+	0.712566i	−0.959614	−	0.281320i	$-0.909228\pi$
$743$	−23.1476	+	19.4231i	−0.849203	+	0.712566i	0.110411	+	0.993886i	$0.464783\pi$
$744$		0			0
$745$	−78.8016	+	28.6814i	−2.88707	+	1.05081i
$746$		0			0
$747$	7.97846	+	19.7245i	0.291917	+	0.721681i
$748$		0			0
$749$	0.0590059	−	0.334639i	0.00215603	−	0.0122274i
$750$		0			0
$751$	−9.26737	−	3.37305i	−0.338171	−	0.123084i	0.167352	−	0.985897i	$-0.446478\pi$
$751$	−9.26737	−	3.37305i	−0.338171	−	0.123084i	−0.505523	+	0.862813i	$0.668701\pi$
$752$		0			0
$753$	−13.7876	−	13.3092i	−0.502449	−	0.485014i
$754$		0			0
$755$	−30.4127			−1.10683
$756$		0			0
$757$	23.7215			0.862171			0.431086	−	0.902311i	$-0.358131\pi$
$757$	23.7215			0.862171			0.431086	+	0.902311i	$0.358131\pi$
$758$		0			0
$759$	23.7965	−	6.82872i	0.863757	−	0.247867i
$760$		0			0
$761$	0.394516	+	0.143592i	0.0143012	+	0.00520521i	0.349161	−	0.937063i	$-0.386467\pi$
$761$	0.394516	+	0.143592i	0.0143012	+	0.00520521i	−0.334860	+	0.942268i	$0.608689\pi$
$762$		0			0
$763$	−0.110599	+	0.627239i	−0.00400396	+	0.0227076i
$764$		0			0
$765$	−4.75647	+	14.6590i	−0.171971	+	0.529998i
$766$		0			0
$767$	57.4521	−	20.9109i	2.07447	−	0.755047i
$768$		0			0
$769$	36.6110	−	30.7203i	1.32023	−	1.10780i	0.333968	−	0.942584i	$-0.391612\pi$
$769$	36.6110	−	30.7203i	1.32023	−	1.10780i	0.986257	−	0.165217i	$-0.0528323\pi$
$770$		0			0
$771$	−14.1600	−	29.0174i	−0.509959	−	1.04504i
$772$		0			0
$773$	15.5336	+	26.9050i	0.558706	+	0.967707i	0.997605	+	0.0691705i	$0.0220352\pi$
$773$	15.5336	+	26.9050i	0.558706	+	0.967707i	−0.438899	+	0.898536i	$0.644631\pi$
$774$		0			0
$775$	7.85154	−	13.5993i	0.282036	−	0.488500i
$776$		0			0
$777$	0.307180	+	2.91696i	0.0110200	+	0.104645i
$778$		0			0
$779$	1.50645	+	8.54351i	0.0539742	+	0.306103i
$780$		0			0
$781$	65.6250	+	55.0659i	2.34825	+	1.97041i
$782$		0			0
$783$	−27.7768	+	3.92091i	−0.992663	+	0.140122i
$784$		0			0
$785$	31.0292	+	26.0366i	1.10748	+	0.929286i
$786$		0			0
$787$	−5.03000	−	28.5266i	−0.179300	−	1.01686i	−0.933062	−	0.359715i	$-0.882874\pi$
$787$	−5.03000	−	28.5266i	−0.179300	−	1.01686i	0.753762	−	0.657147i	$-0.228237\pi$
$788$		0			0
$789$	−5.77026	−	2.56769i	−0.205427	−	0.0914123i
$790$		0			0
$791$	6.35155	−	11.0012i	0.225835	−	0.391158i
$792$		0			0
$793$	13.6715	+	23.6797i	0.485488	+	0.840891i
$794$		0			0
$795$	−25.7855	+	38.2452i	−0.914518	+	1.35642i
$796$		0			0
$797$	11.8692	−	9.95943i	0.420428	−	0.352781i	−0.407898	−	0.913028i	$-0.633738\pi$
$797$	11.8692	−	9.95943i	0.420428	−	0.352781i	0.828326	+	0.560247i	$0.189294\pi$
$798$		0			0
$799$	−14.2777	+	5.19667i	−0.505110	+	0.183845i
$800$		0			0
$801$	20.9601	−	13.1090i	0.740587	−	0.463185i
$802$		0			0
$803$	9.10236	−	51.6220i	0.321215	−	1.82170i
$804$		0			0
$805$	−6.28510	−	2.28759i	−0.221521	−	0.0806269i
$806$		0			0
$807$	9.61986	−	38.6163i	0.338635	−	1.35936i
$808$		0			0
$809$	51.1201			1.79729			0.898644	−	0.438680i	$-0.144554\pi$
$809$	51.1201			1.79729			0.898644	+	0.438680i	$0.144554\pi$
$810$		0			0
$811$	43.8131			1.53849			0.769243	−	0.638956i	$-0.220633\pi$
$811$	43.8131			1.53849			0.769243	+	0.638956i	$0.220633\pi$
$812$		0			0
$813$	0.492428	−	1.97672i	0.0172702	−	0.0693265i
$814$		0			0
$815$	−52.5566	−	19.1291i	−1.84098	−	0.670062i
$816$		0			0
$817$	−5.89370	+	33.4248i	−0.206194	+	1.16939i
$818$		0			0
$819$	0.395120	+	11.1854i	0.0138066	+	0.390851i
$820$		0			0
$821$	10.7613	−	3.91680i	0.375573	−	0.136697i	−0.147335	−	0.989087i	$-0.547070\pi$
$821$	10.7613	−	3.91680i	0.375573	−	0.136697i	0.522908	+	0.852389i	$0.324847\pi$
$822$		0			0
$823$	37.2376	−	31.2461i	1.29802	−	1.08917i	0.307538	−	0.951536i	$-0.400495\pi$
$823$	37.2376	−	31.2461i	1.29802	−	1.08917i	0.990483	−	0.137634i	$-0.0439497\pi$
$824$		0			0
$825$	54.5220	−	80.8674i	1.89821	−	2.81544i
$826$		0			0
$827$	−6.67797	−	11.5666i	−0.232216	−	0.402209i	0.726244	−	0.687437i	$-0.241264\pi$
$827$	−6.67797	−	11.5666i	−0.232216	−	0.402209i	−0.958460	+	0.285227i	$0.907931\pi$
$828$		0			0
$829$	1.27452	−	2.20753i	0.0442659	−	0.0766708i	−0.843044	−	0.537845i	$-0.819238\pi$
$829$	1.27452	−	2.20753i	0.0442659	−	0.0766708i	0.887309	+	0.461174i	$0.152572\pi$
$830$		0			0
$831$	42.9019	+	19.0908i	1.48825	+	0.662253i
$832$		0			0
$833$	−1.51997	−	8.62017i	−0.0526638	−	0.298671i
$834$		0			0
$835$	9.62634	+	8.07746i	0.333133	+	0.279532i
$836$		0			0
$837$	7.50340	+	4.68234i	0.259356	+	0.161845i
$838$		0			0
$839$	32.7106	+	27.4475i	1.12930	+	0.947592i	0.999036	−	0.0438877i	$-0.0139744\pi$
$839$	32.7106	+	27.4475i	1.12930	+	0.947592i	0.130260	+	0.991480i	$0.458419\pi$
$840$		0			0
$841$	0.0252522	+	0.143212i	0.000870766	+	0.00493836i
$842$		0			0
$843$	1.64909	+	15.6597i	0.0567976	+	0.539347i
$844$		0			0
$845$	21.2588	−	36.8213i	0.731324	−	1.26669i
$846$		0			0
$847$	9.94048	+	17.2174i	0.341559	+	0.591598i
$848$		0			0
$849$	22.6503	+	46.4162i	0.777355	+	1.59300i
$850$		0			0
$851$	−4.01167	+	3.36619i	−0.137518	+	0.115392i
$852$		0			0
$853$	27.7382	−	10.0959i	0.949737	−	0.345676i	0.179734	−	0.983715i	$-0.442476\pi$
$853$	27.7382	−	10.0959i	0.949737	−	0.345676i	0.770004	+	0.638039i	$0.220254\pi$
$854$		0			0
$855$	−60.0243	+	12.7839i	−2.05279	+	0.437198i
$856$		0			0
$857$	−9.49801	+	53.8659i	−0.324446	+	1.84002i	0.189095	+	0.981959i	$0.439445\pi$
$857$	−9.49801	+	53.8659i	−0.324446	+	1.84002i	−0.513541	+	0.858065i	$0.671667\pi$
$858$		0			0
$859$	−2.30867	−	0.840289i	−0.0787710	−	0.0286703i	0.302334	−	0.953202i	$-0.402234\pi$
$859$	−2.30867	−	0.840289i	−0.0787710	−	0.0286703i	−0.381105	+	0.924532i	$0.624456\pi$
$860$		0			0
$861$	−2.01651	+	0.578665i	−0.0687225	+	0.0197209i
$862$		0			0
$863$	−2.81820			−0.0959325			−0.0479663	−	0.998849i	$-0.515274\pi$
$863$	−2.81820			−0.0959325			−0.0479663	+	0.998849i	$0.515274\pi$
$864$		0			0
$865$	−53.2954			−1.81210
$866$		0			0
$867$	−18.8732	−	18.2183i	−0.640967	−	0.618725i
$868$		0			0
$869$	−26.2580	−	9.55711i	−0.890740	−	0.324203i
$870$		0			0
$871$	0.0486257	−	0.275770i	0.00164762	−	0.00934412i
$872$		0			0
$873$	−8.38180	−	1.17454i	−0.283681	−	0.0397521i
$874$		0			0
$875$	−11.3409	+	4.12776i	−0.383393	+	0.139544i
$876$		0			0
$877$	10.9791	−	9.21252i	0.370736	−	0.311085i	−0.438316	−	0.898821i	$-0.644425\pi$
$877$	10.9791	−	9.21252i	0.370736	−	0.311085i	0.809053	+	0.587736i	$0.199981\pi$
$878$		0			0
$879$	−13.0575	−	0.910428i	−0.440420	−	0.0307080i
$880$		0			0
$881$	−1.44711	−	2.50647i	−0.0487543	−	0.0844450i	0.840618	−	0.541628i	$-0.182192\pi$
$881$	−1.44711	−	2.50647i	−0.0487543	−	0.0844450i	−0.889373	+	0.457183i	$0.848858\pi$
$882$		0			0
$883$	−9.66057	+	16.7326i	−0.325104	+	0.563097i	−0.981533	−	0.191291i	$-0.938733\pi$
$883$	−9.66057	+	16.7326i	−0.325104	+	0.563097i	0.656429	+	0.754388i	$0.272066\pi$
$884$		0			0
$885$	−65.5766	+	47.6644i	−2.20433	+	1.60222i
$886$		0			0
$887$	6.50951	+	36.9173i	0.218568	+	1.23956i	0.874606	+	0.484834i	$0.161120\pi$
$887$	6.50951	+	36.9173i	0.218568	+	1.23956i	−0.656038	+	0.754727i	$0.727769\pi$
$888$		0			0
$889$	−2.54648	−	2.13675i	−0.0854061	−	0.0716642i
$890$		0			0
$891$	44.4673	+	32.2526i	1.48971	+	1.08050i
$892$		0			0
$893$	−46.3496	−	38.8919i	−1.55103	−	1.30147i
$894$		0			0
$895$	−5.19839	−	29.4815i	−0.173763	−	0.985459i
$896$		0			0
$897$	−16.1646	+	11.7492i	−0.539719	+	0.392295i
$898$		0			0
$899$	4.59459	−	7.95807i	0.153238	−	0.265416i
$900$		0			0
$901$	4.80844	+	8.32846i	0.160192	+	0.277461i
$902$		0			0
$903$	−8.18774	−	0.570884i	−0.272471	−	0.0189978i
$904$		0			0
$905$	10.6112	−	8.90383i	0.352727	−	0.295973i
$906$		0			0
$907$	−14.1869	+	5.16363i	−0.471070	+	0.171455i	−0.566637	−	0.823968i	$-0.691756\pi$
$907$	−14.1869	+	5.16363i	−0.471070	+	0.171455i	0.0955671	+	0.995423i	$0.469534\pi$
$908$		0			0
$909$	−9.10536	+	11.6640i	−0.302006	+	0.386871i
$910$		0			0
$911$	7.70696	−	43.7083i	0.255343	−	1.44812i	−0.539848	−	0.841762i	$-0.681518\pi$
$911$	7.70696	−	43.7083i	0.255343	−	1.44812i	0.795191	−	0.606359i	$-0.207371\pi$
$912$		0			0
$913$	−40.6782	−	14.8056i	−1.34625	−	0.489995i
$914$		0			0
$915$	−26.0855	−	25.1803i	−0.862360	−	0.832436i
$916$		0			0
$917$	−15.2874			−0.504833
$918$		0			0
$919$	−15.2325			−0.502474			−0.251237	−	0.967926i	$-0.580837\pi$
$919$	−15.2325			−0.502474			−0.251237	+	0.967926i	$0.580837\pi$
$920$		0			0
$921$	−7.93730	+	2.27772i	−0.261543	+	0.0750533i
$922$		0			0
$923$	−64.9793	−	23.6505i	−2.13882	−	0.778467i
$924$		0			0
$925$	−3.58250	+	20.3174i	−0.117792	+	0.668031i
$926$		0			0
$927$	26.8114	+	29.7529i	0.880601	+	0.977214i
$928$		0			0
$929$	31.9975	−	11.6461i	1.04980	−	0.382097i	0.241215	−	0.970472i	$-0.422454\pi$
$929$	31.9975	−	11.6461i	1.04980	−	0.382097i	0.808589	+	0.588374i	$0.200232\pi$
$930$		0			0
$931$	26.7016	−	22.4053i	0.875108	−	0.734303i
$932$		0			0
$933$	−1.36492	−	2.79707i	−0.0446854	−	0.0915718i
$934$		0			0
$935$	−15.6775	−	27.1542i	−0.512709	−	0.888038i
$936$		0			0
$937$	10.4487	−	18.0976i	0.341343	−	0.591223i	−0.643340	−	0.765581i	$-0.722452\pi$
$937$	10.4487	−	18.0976i	0.341343	−	0.591223i	0.984682	+	0.174358i	$0.0557850\pi$
$938$		0			0
$939$	−2.84064	−	26.9746i	−0.0927008	−	0.880282i
$940$		0			0
$941$	−4.59174	−	26.0411i	−0.149687	−	0.848915i	−0.963484	−	0.267766i	$-0.913715\pi$
$941$	−4.59174	−	26.0411i	−0.149687	−	0.848915i	0.813797	−	0.581149i	$-0.197396\pi$
$942$		0			0
$943$	−2.86935	−	2.40767i	−0.0934390	−	0.0784047i
$944$		0			0
$945$	−4.59461	−	14.1117i	−0.149463	−	0.459054i
$946$		0			0
$947$	−10.4158	−	8.73993i	−0.338469	−	0.284010i	0.457671	−	0.889122i	$-0.348684\pi$
$947$	−10.4158	−	8.73993i	−0.338469	−	0.284010i	−0.796140	+	0.605112i	$0.793128\pi$
$948$		0			0
$949$	7.34730	+	41.6686i	0.238503	+	1.35262i
$950$		0			0
$951$	27.1925	+	12.1003i	0.881776	+	0.392379i
$952$		0			0
$953$	−2.31679	+	4.01280i	−0.0750483	+	0.129987i	−0.901107	−	0.433596i	$-0.857244\pi$
$953$	−2.31679	+	4.01280i	−0.0750483	+	0.129987i	0.826059	+	0.563584i	$0.190578\pi$
$954$		0			0
$955$	−24.9723	−	43.2532i	−0.808084	−	1.39964i
$956$		0			0
$957$	31.9054	−	47.3222i	1.03135	−	1.52971i
$958$		0			0
$959$	−6.61290	+	5.54888i	−0.213542	+	0.179183i
$960$		0			0
$961$	26.4080	−	9.61171i	0.851870	−	0.310055i
$962$		0			0
$963$	1.18886	+	0.631515i	0.0383106	+	0.0203503i
$964$		0			0
$965$	−14.4788	+	82.1132i	−0.466088	+	2.64332i
$966$		0			0
$967$	23.0435	+	8.38714i	0.741029	+	0.269712i	0.684826	−	0.728707i	$-0.259878\pi$
$967$	23.0435	+	8.38714i	0.741029	+	0.269712i	0.0562030	+	0.998419i	$0.482101\pi$
$968$		0			0
$969$	−3.09296	+	12.4158i	−0.0993601	+	0.398854i
$970$		0			0
$971$	−5.11105			−0.164021			−0.0820106	−	0.996631i	$-0.526134\pi$
$971$	−5.11105			−0.164021			−0.0820106	+	0.996631i	$0.526134\pi$
$972$		0			0
$973$	−8.02133			−0.257152
$974$		0			0
$975$	−19.0300	+	76.3906i	−0.609447	+	2.44646i
$976$		0			0
$977$	44.4768	+	16.1882i	1.42294	+	0.517907i	0.934899	−	0.354914i	$-0.115490\pi$
$977$	44.4768	+	16.1882i	1.42294	+	0.517907i	0.488040	+	0.872821i	$0.337712\pi$
$978$		0			0
$979$	−8.73407	+	49.5334i	−0.279142	+	1.58309i
$980$		0			0
$981$	−2.22838	−	1.18370i	−0.0711466	−	0.0377925i
$982$		0			0
$983$	−9.99048	+	3.63624i	−0.318647	+	0.115978i	−0.496392	−	0.868099i	$-0.665342\pi$
$983$	−9.99048	+	3.63624i	−0.318647	+	0.115978i	0.177745	+	0.984077i	$0.443120\pi$
$984$		0			0
$985$	−33.8404	+	28.3954i	−1.07824	+	0.904754i
$986$		0			0
$987$	8.17943	−	12.1318i	0.260354	−	0.386159i
$988$		0			0
$989$	−7.32711	−	12.6909i	−0.232989	−	0.403548i
$990$		0			0
$991$	1.69168	−	2.93008i	0.0537380	−	0.0930770i	−0.837905	−	0.545816i	$-0.816220\pi$
$991$	1.69168	−	2.93008i	0.0537380	−	0.0930770i	0.891643	+	0.452739i	$0.149553\pi$
$992$		0			0
$993$	−39.2979	−	17.4870i	−1.24708	−	0.554935i
$994$		0			0
$995$	11.5969	+	65.7691i	0.367645	+	2.08502i
$996$		0			0
$997$	3.53265	+	2.96425i	0.111880	+	0.0938786i	0.697012	−	0.717060i	$-0.254513\pi$
$997$	3.53265	+	2.96425i	0.111880	+	0.0938786i	−0.585131	+	0.810939i	$0.698957\pi$
$998$		0			0
$999$	−11.3675	−	2.40905i	−0.359651	−	0.0762190i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.y.a.97.5	yes	48
4.3	odd	2	inner	864.2.y.a.97.4	✓	48
27.22	even	9	inner	864.2.y.a.481.5	yes	48
108.103	odd	18	inner	864.2.y.a.481.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.y.a.97.4	✓	48	4.3	odd	2	inner
864.2.y.a.97.5	yes	48	1.1	even	1	trivial
864.2.y.a.481.4	yes	48	108.103	odd	18	inner
864.2.y.a.481.5	yes	48	27.22	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.y (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.418682 - 1.68069i) q^{3} +(3.54422 + 1.28999i) q^{5} +(-0.131496 + 0.745751i) q^{7} +(-2.64941 - 1.40735i) q^{9} +O(q^{10})\)	\(q+(0.418682 - 1.68069i) q^{3} +(3.54422 + 1.28999i) q^{5} +(-0.131496 + 0.745751i) q^{7} +(-2.64941 - 1.40735i) q^{9} +(5.73551 - 2.08756i) q^{11} +(-3.77411 + 3.16685i) q^{13} +(3.65197 - 5.41662i) q^{15} +(-0.681013 - 1.17955i) q^{17} +(2.71190 - 4.69715i) q^{19} +(1.19832 + 0.533236i) q^{21} +(0.406649 + 2.30622i) q^{23} +(7.06720 + 5.93008i) q^{25} +(-3.47457 + 3.86360i) q^{27} +(4.13561 + 3.47019i) q^{29} +(-0.295571 - 1.67627i) q^{31} +(-1.10717 - 10.5136i) q^{33} +(-1.42806 + 2.47348i) q^{35} +(1.11813 + 1.93666i) q^{37} +(3.74233 + 7.66899i) q^{39} +(-1.22528 + 1.02813i) q^{41} +(-5.88030 + 2.14026i) q^{43} +(-7.57463 - 8.40566i) q^{45} +(1.93713 - 10.9860i) q^{47} +(6.03899 + 2.19801i) q^{49} +(-2.26758 + 0.650713i) q^{51} -7.06071 q^{53} +23.0208 q^{55} +(-6.75901 - 6.52447i) q^{57} +(-11.6613 - 4.24435i) q^{59} +(0.963730 - 5.46558i) q^{61} +(1.39792 - 1.79074i) q^{63} +(-17.4615 + 6.35546i) q^{65} +(-0.0435401 + 0.0365345i) q^{67} +(4.04629 + 0.282124i) q^{69} +(7.01777 + 12.1551i) q^{71} +(4.29405 - 7.43752i) q^{73} +(12.9255 - 9.39492i) q^{75} +(0.802600 + 4.55177i) q^{77} +(-3.50706 - 2.94277i) q^{79} +(5.03875 + 7.45728i) q^{81} +(-5.43304 - 4.55887i) q^{83} +(-0.892053 - 5.05908i) q^{85} +(7.56380 - 5.49775i) q^{87} +(-4.12031 + 7.13659i) q^{89} +(-1.86540 - 3.23097i) q^{91} +(-2.94103 - 0.205061i) q^{93} +(15.6708 - 13.1494i) q^{95} +(2.65109 - 0.964918i) q^{97} +(-18.1336 - 2.54106i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{9}+O(q^{10}) \) 48 * q - 12 * q^9	\( 48 q - 12 q^{9} - 12 q^{17} - 48 q^{21} + 24 q^{25} + 6 q^{29} - 6 q^{33} + 30 q^{37} - 12 q^{41} + 30 q^{45} - 6 q^{49} - 36 q^{53} - 6 q^{57} - 12 q^{61} - 60 q^{65} - 78 q^{69} + 48 q^{73} - 12 q^{77} - 36 q^{81} + 102 q^{85} - 66 q^{89} + 36 q^{93} + 6 q^{97}+O(q^{100}) \) 48 * q - 12 * q^9 - 12 * q^17 - 48 * q^21 + 24 * q^25 + 6 * q^29 - 6 * q^33 + 30 * q^37 - 12 * q^41 + 30 * q^45 - 6 * q^49 - 36 * q^53 - 6 * q^57 - 12 * q^61 - 60 * q^65 - 78 * q^69 + 48 * q^73 - 12 * q^77 - 36 * q^81 + 102 * q^85 - 66 * q^89 + 36 * q^93 + 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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